Problem:
At Rachelle's school an A counts 4 points, a B 3 points, a C 2 points, and a D 1 point. Her GPA on the four classes she is taking is computed as the total sum of points divided by 4 . She is certain that she will get As in both Mathematics and Science, and at least a in each of English and History. She thinks she has a chance of getting an A in English, and a chance of getting a B. In History, she has a chance of getting an A, and a chance of getting a B, independently of what she gets in English. What is the probability that Rachelle will get a GPA of at least 3.5 ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Rachelle needs a total of at least 14 points to get a 3.5 or higher GPA, so she needs a total of at least 6 points in English and History. The probability of a in English is , and the probability of a in History is . The probability that Rachelle earns exactly 6,7 , or 8 total points is computed as follows:
The probability that Rachelle will get at least a 3.5 GPA is
The problems on this page are the property of the MAA's American Mathematics Competitions